The present version of the GM model considers a population of an
infinite number of informed traders who behave in a competitive
fashion. The situation is very different from that of a single
informed trader, who trades with frequency \(\nu \) . In the latter case,
the GM model becomes a repeated game of incomplete
information [1]} between the market maker and the
informed trader. In this setting, the informed trader may choose
not to reveal information to the market maker, with
her trading activity. For example, the informed trader may decide to
act according to her private information with probability \(c\) 
and act as a noise trader with probability \(1-c\) , in order to conceal
her information. This changes the statistics of the trading
activity, because in practice \(\nu \rightarrow c \nu \)  and hence the temperature
\(T(\nu )\rightarrow T(c\nu )\) . With this strategy, the informed trader would
also share a fraction \((1-c)\nu /(1-c\nu )\)  of the losses of noise
traders. Hence their gain would satisfy the bound
\(\mathbb {E}[G^{\prime }]\le \frac{1-\nu }{1-c\nu }\,T(c\nu )H[Y]\) . This shows that by
taking an infinitesimally small value of \(c\) , noise traders could
access the regime where the inequality holds asymptotically as an equality,
and increase their gain by making the market temperature \(T(c\nu )\) 
arbitrarily large. This argument
suggests further avenues along which the results of the present paper
could be extended.
